The phenomenological single-nucleon potential constructed in this way may provide a convenient starting point for studying astrophysical problems when the detailed information related to finite nuclei is irrelevant [1]}, [2]}, [3]}.
For non-relativistic applications, the EOS of ANM could be treated as an expansion on \(k_{\mathrm {F}}/M\)  or equivalently on \(\rho /\rho _0\)  [4]}, the single-nucleon potential based on this idea adopted here takes the following form,
\({U_J}(\rho ,\delta ,|\mathbf {k}|)=&\alpha \left(\frac{\rho }{\rho _0}\right)+\left(\beta +\beta _{\mathrm {IS}}e^{\Gamma _{4/3}\tau _3^J\delta }\right)\left(\frac{\rho }{\rho _0}\right)^{4/3}\\&+\left(\lambda +\lambda _{\mathrm {IS}}e^{\Gamma _{5/3}\tau _3^J\delta }\right)\left(\frac{\rho }{\rho _0}\right)^{5/3}+\phi \left(\frac{\rho }{\rho _0}\right)^2+\mu \left(\frac{\rho }{\rho _0}\right)\left(1+\frac{\theta |\mathbf {k}|^3}{\Lambda ^3}\right)^{-1}.\) 
